Question

edwards grandmother used to make him pannukakku when he was little. he wants to surprise her by making it himself. the recipe he found requires a 9 - in. by 13 - in. rectangular pan. edward would like to use a round cast iron pan like his grandmother does.
what is the area of a 9 - in. by 13 - in. pan?
117 in.²
edward has four round pans, each with a different radius. he needs to use the pan that is closest in area to the rectangular pan. which pan should edward use?
a pan with a radius of 4 in.
a pan with a radius of 6 in.
a pan with a radius of 8 in.
a pan with a radius of 10 in.

Explanation:

for a rectangle is $A = l\times w$. Given $l = 13$ in and $w=9$ in, then $A=13\times9 = 117$ in².

Step2: Calculate areas of round pans

The area formula for a circle is $A=\pi r^{2}$.

• For $r = 4$ in, $A_1=\pi\times4^{2}=16\pi\approx16\times 3.14 = 50.24$ in².
• For $r = 6$ in, $A_2=\pi\times6^{2}=36\pi\approx36\times3.14 = 113.04$ in².
• For $r = 8$ in, $A_3=\pi\times8^{2}=64\pi\approx64\times3.14 = 200.96$ in².
• For $r = 10$ in, $A_4=\pi\times10^{2}=100\pi\approx100\times3.14 = 314$ in².

Step3: Compare areas

The difference between the area of the rectangular pan ($117$ in²) and $A_1$ is $|117 - 50.24|=66.76$ in².
The difference between the area of the rectangular pan and $A_2$ is $|117 - 113.04| = 3.96$ in².
The difference between the area of the rectangular pan and $A_3$ is $|117 - 200.96|=83.96$ in².
The difference between the area of the rectangular pan and $A_4$ is $|117 - 314|=197$ in².
Since $3.96$ is the smallest difference, the pan with a radius of 6 in is closest in area to the rectangular pan.

Answer:

for a rectangle is $A = l\times w$. Given $l = 13$ in and $w=9$ in, then $A=13\times9 = 117$ in².

Step2: Calculate areas of round pans

The area formula for a circle is $A=\pi r^{2}$.

• For $r = 4$ in, $A_1=\pi\times4^{2}=16\pi\approx16\times 3.14 = 50.24$ in².
• For $r = 6$ in, $A_2=\pi\times6^{2}=36\pi\approx36\times3.14 = 113.04$ in².
• For $r = 8$ in, $A_3=\pi\times8^{2}=64\pi\approx64\times3.14 = 200.96$ in².
• For $r = 10$ in, $A_4=\pi\times10^{2}=100\pi\approx100\times3.14 = 314$ in².

Step3: Compare areas

The difference between the area of the rectangular pan ($117$ in²) and $A_1$ is $|117 - 50.24|=66.76$ in².
The difference between the area of the rectangular pan and $A_2$ is $|117 - 113.04| = 3.96$ in².
The difference between the area of the rectangular pan and $A_3$ is $|117 - 200.96|=83.96$ in².
The difference between the area of the rectangular pan and $A_4$ is $|117 - 314|=197$ in².
Since $3.96$ is the smallest difference, the pan with a radius of 6 in is closest in area to the rectangular pan.